Chapter 4.5, Problem 12CE

To determine

To find: congruent criteria used to prove that the triangles are congruent.

Answer to Problem 12CE

Triangle are congruent by HL congruence criteria

  $\Delta WUY,\Delta ZVX$ is a pair of overlapping triangles.

Explanation of Solution

Given information: $\overline{WU}\cong \overline{ZV}$ and $\overline{WX}=\overline{YZ}$ . $\angle U,\angle V$ are right angles

  

Consider $\Delta WUY,\Delta ZVX$

  $\overline{WU}\cong \overline{VZ}$ (Given)

As $\angle U,\angle V$ are right angles,

  $\angle U\cong \angle V$ (right angles are congruent)

  $\overline{WX}=\overline{YZ}$ (Given)

Add $\overline{XY}$ to both sides.

  $\begin{array}{l}\overline{WX}+\overline{XY}=\overline{YZ}+\overline{XY}\\ \Rightarrow \overline{WY}=\overline{XZ}\end{array}$

So,

  $\overline{WY}\cong \overline{XZ}$ (line segments of equal measures are congruent)

Therefore,

  $\Delta WUY,\Delta ZVX$ (RHS congruence criteria)

Also,

Congruent triangles basically overlap each other.

So, $\Delta WUY,\Delta ZVX$ is a pair of overlapping triangles.